A comment concerning \(\epsilon ^{\mu \nu \rho \sigma }\)  is appropriate here.
The above polarization state vectors will be eventually used in D-dimensional calculations.
To this end, following [1]}, [2]}, [3]},
we will treat \(\epsilon ^{\mu \nu \rho \sigma }\)  merely as a symbol denoting an object whose
algebraic manipulation rules consist of the following two statements.
